2.3 Algebra & Data Interpretation
Key Takeaways
- Algebra is about 7 items (~18%): one- and two-step equations, evaluating expressions, and inequalities
- Data & Information is about 7 items (~18%) and is NEW on the NEX — it was not on the older PAX exam
- Solve equations by isolating the variable with inverse operations applied equally to both sides
- Mean = sum / count; median = middle of ordered data; mode = most frequent value; range = max - min
- Bar graphs compare categories, line graphs show trends over time, pie charts show parts of a whole
- When dividing or multiplying an inequality by a negative number, flip the inequality symbol
- Always read the title, axis labels, units, and scale before answering any graph or table question
- For word problems: identify the unknown, extract the numbers, build the equation, solve, then check reasonableness
Algebra on the NLN NEX (~7 items)
NEX algebra centers on solving for one variable. The governing rule: whatever you do to one side, do to the other.
One-step equations
| Form | Inverse operation | Example |
|---|---|---|
| x + a = b | Subtract a | x + 7 = 15 -> x = 8 |
| x - a = b | Add a | x - 3 = 12 -> x = 15 |
| ax = b | Divide by a | 4x = 28 -> x = 7 |
| x/a = b | Multiply by a | x/5 = 6 -> x = 30 |
Two-step equations
Undo addition/subtraction first, then multiplication/division.
3x + 5 = 20 -> subtract 5: 3x = 15 -> divide by 3: x = 5.
Nursing-flavored example: a nurse earns $28/hour for x hours, then a $28 meal fee is deducted, leaving $476. 28x - 28 = 476 -> 28x = 504 -> x = 18 hours.
Evaluating expressions
Substitute the given values and simplify carefully — watch the signs. If a = 3 and b = 4, then 2a + 3b - 5 = 6 + 12 - 5 = 13. With negatives, subtracting a negative becomes addition.
Inequalities
| Symbol | Meaning | Example |
|---|---|---|
| < | less than | x < 5 |
| > | greater than | x > 10 |
| <= | less than or equal | x <= 3 |
| >= | greater than or equal | x >= 7 |
Clinical use: a normal serum potassium is 3.5 <= K <= 5.0 mEq/L. A value of 5.4 violates the upper bound and signals hyperkalemia.
Critical rule: when you multiply or divide both sides by a negative number, reverse the inequality sign. Example: -2x < 6 -> divide by -2 and flip -> x > -3.
Setting up word problems
- Identify exactly what is asked (the unknown).
- Translate each phrase into math: of means multiply, per means divide, is means equals.
- Build one equation, solve, then check the answer is reasonable (a nurse working 200 hours/week is impossible).
This structured approach prevents the most common NEX algebra mistake: solving for the wrong quantity.
Translating common phrases
| Phrase | Operation |
|---|---|
| sum, increased by, more than | addition |
| difference, decreased by, less than | subtraction |
| product, of, times, twice | multiplication |
| quotient, per, ratio, divided by | division |
| is, was, results in, equals | = |
Watch the order with 'less than': 7 less than x is x - 7, not 7 - x. Reversing it is a classic distractor on the NEX.
Data & Information (~7 items) — NEW on the NEX
This subsection is new to the NEX and absent from the old PAX. It tests data literacy: reading displays and computing simple statistics.
Data displays
| Display | Best for | What to read |
|---|---|---|
| Bar graph | Comparing categories | Bar heights and differences |
| Line graph | Trends over time | Slope and direction |
| Pie chart | Parts of a whole | Slice size; percentages sum to 100 |
| Table | Exact values | Row/column labels |
| Scatter plot | Correlation of two variables | Pattern direction and clustering |
Measures of central tendency
| Measure | Definition | When it is best |
|---|---|---|
| Mean | Sum / count | Evenly distributed data |
| Median | Middle of ordered data | Data with outliers (e.g., one very high value) |
| Mode | Most frequent value | Categorical or most-common data |
| Range | Max - Min | Quick spread |
Worked set — pain scores 3, 5, 7, 5, 8, 5, 6: ordered = 3, 5, 5, 5, 6, 7, 8. Mean = 39/7 = 5.57; median = 5 (4th of 7); mode = 5 (appears 3x); range = 8 - 3 = 5. A single outlier pulls the mean but not the median — that is why median is preferred for skewed data.
Reading graphs and tables under time pressure
Work the display in a fixed order so you never misread a question:
- Title — what is being measured?
- Axes and labels — what units (mg, mL, beats/min, days)?
- Scale — are the intervals equal, and does the y-axis start at zero? A truncated axis exaggerates small changes.
- Trend — increasing, decreasing, stable, or fluctuating?
- Answer only what is asked — do not extrapolate beyond the plotted data.
Rate of change from a line graph: weight rising from 150 lb in January to 165 lb in June is a 15 lb gain over 5 intervals (Jan->Jun), so 3 lb/month. Count intervals between points, not the number of months listed.
Trap: confusing the mean and the median. If a question gives an ordered list and asks for the middle value, the answer is the median even when an outlier makes the mean look more 'reasonable.' Read the requested statistic precisely before computing.
Solve for x: 5x - 12 = 33
A patient's heart rates over six readings are 72, 80, 68, 76, 84, 72. What is the mode?
A line graph shows weight rising from 150 lb in January to 165 lb in June. What was the average monthly gain?
If a = 4 and b = -2, what is the value of 3a - 2b + 5?
Blood glucose readings over five days are 95, 130, 88, 110, 95. What is the median?
The difference between the maximum and minimum values in a data set is called the _____.
Type your answer below
A nurse earns $32 per hour, with overtime at 1.5x for hours over 40. She works 36 hours in week 1 and 44 hours in week 2. What are her total earnings?
Which statements about the data set {4, 7, 7, 9, 12, 15} are TRUE? (Select all that apply)
Select all that apply